6 problems

Transcendence-degree realization conjecture. If

Let $\rK$ be the base field. For $d\in\N$, an $\rsg{d}$ configuration is a configuration $\cF$ of polynomials as defined in the cited formulation of Gupta's conjecture; its transce…

Gupta's bounded transcendence-degree conjecture. There is a function $\lambda$ such that

Let $R$ be a ring equipped with a monomial ordering … trdeg of $R$. Monomial-ordering transcendence-degree conjecture. The statements denoted by TheoremtMain, equations(tMainA) and…

Let $K$ be a field of characteristic $\operatorname{ch}(K)$, and let $R_{\delta}(k,s)$ strictly upper-bound the rank of any minimal and simple $\Sigma\Pi_{\delta}\Sigma\Pi(k,s,n)$…

Consider algebraic cycles in Abel–Jacobi kernels, and define their transcendence degree by the field of definition of the cycles. Beilinson's conjecture. There are no non-trivial a…